Spiral Curves

Spiral curves (aka transition or easement curves) are generally used to provide a gradual transition in curvature from a straight section of road to a curved section (or from tangents to circular curves). Figure 1 shows the placement of spiral curves in relation to circular curves. Figure 2 shows the components of a spiral curve. Spiral curves are necessary on high-speed roads from the standpoint of comfortable operation and gradually bringing about the full superelevation? of the curves. A spiral should be utilized with a circular curve with a superelevation? of 3% or greater. Spiral curves were developed for locomotives and are still used widely today in the industry.

Figure 1: The Placement of a Spiral Curve

Figure 2: Components of a Spiral Curve[2]

Definitions [1]:

SCS PI = Point of intersection of main tangents.

TS = Point of change from tangent to spiral curve.

SC = Point of change from spiral curve to circular curve.

CS = Point of change from circular curve to spiral curve.

ST = Point of change from spiral curve to tangent.

LC = Long chord.

LT = Long tangent.

ST = Short tangent.

PC = Point of curvature for the adjoining circular curve.

PT = Point of tangency for the adjoining circular curve.

Ts = Tangent distance from TS to SCS PI or ST to SCS PI.

Es = External distance from the SCS PI to the center of the circular curve.

Rc = Radius of the adjoining circular curve.

Dc = Degree of curve of the adjoining circular curve, based on a 100 foot arc (English units only).

D = Degree of curve of the spiral at any point, based on a 100 foot arc (English units only).

l = Spiral arc from the TS to any point on the spiral (l = ls at the SC).